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library(priorsense)
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library(bayestestR)
df <- read_xlsx("hair_cort_dog_all.xlsx", col_types = c("text", "text",
"text", "text", "text", "text",
"text", "numeric","text", "skip",
"numeric", "skip", "skip",
"numeric", "skip"))
df <- as.data.frame(df)
dim(df) # will tell you how many rows and columns the dataset has
## [1] 73 11
class(df) # will tell you what data structure has the dataset been assigned
## [1] "data.frame"
head(df)
## number group visit season breed_group coat_colour sex age comorbidity
## 1 c1 stopped v0 winter ret dark Male 43 yes
## 2 c2 stopped v0 autumn mix dark Male 105 yes
## 3 c3 stopped v0 spring ckcs mix Female 117 yes
## 4 c4 stopped v0 summer ret dark Female 108 yes
## 5 c5 stopped v0 summer ret dark Female 110 yes
## 6 c6 stopped v0 winter mix light Female 120 yes
## fat_percent cortisol
## 1 52.21393 4.924220
## 2 38.52059 7.304202
## 3 46.94916 1.590000
## 4 44.46813 0.861570
## 5 39.59363 6.217317
## 6 NA 4.426785
numeric_df <- Filter(is.numeric, df)
describe(numeric_df) # the describe function in psych provides summary stats
## # A tibble: 3 × 26
## described_variables n na mean sd se_mean IQR skewness kurtosis
## <chr> <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 age 73 0 95.8 35.6 4.16 44 -0.104 -0.00589
## 2 fat_percent 55 18 40.5 7.82 1.05 7.82 -0.294 1.12
## 3 cortisol 73 0 8.11 16.5 1.93 5.43 4.05 18.7
## # ℹ 17 more variables: p00 <dbl>, p01 <dbl>, p05 <dbl>, p10 <dbl>, p20 <dbl>,
## # p25 <dbl>, p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>,
## # p75 <dbl>, p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>
plot_normality(numeric_df)
apply(numeric_df, 2, shapiro.test)
## $age
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.97361, p-value = 0.1288
##
##
## $fat_percent
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.97956, p-value = 0.4692
##
##
## $cortisol
##
## Shapiro-Wilk normality test
##
## data: newX[, i]
## W = 0.46269, p-value = 6.756e-15
qqnorm(df$cortisol)
qqline(df$cortisol, col = "red")
qqnorm(log(df$cortisol))
qqline(log(df$cortisol), col = "red")
shapiro.test(log(df$cortisol))
##
## Shapiro-Wilk normality test
##
## data: log(df$cortisol)
## W = 0.94725, p-value = 0.004126
summary(df$cortisol)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.4141 1.4119 2.3331 8.1089 6.8455 104.6172
summary(log(df$cortisol))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.8817 0.3449 0.8472 1.1816 1.9236 4.6503
df$lgCort <- log(df$cortisol)
summary(df$lgCort)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.8817 0.3449 0.8472 1.1816 1.9236 4.6503
hist(df$lgCort)
df$breed <- df$breed_group
df$breed <- factor(df$breed, levels = c("mix", "ckcs", "pug", "ret", "other"))
head(df$breed)
## [1] ret mix ckcs ret ret mix
## Levels: mix ckcs pug ret other
df$season <- factor(df$season, levels = c("spring", "summer", "autumn", "winter"))
head(df$season)
## [1] winter autumn spring summer summer winter
## Levels: spring summer autumn winter
sumtable(df)
| Variable | N | Mean | Std. Dev. | Min | Pctl. 25 | Pctl. 75 | Max |
|---|---|---|---|---|---|---|---|
| group | 73 | ||||||
| … completed | 42 | 58% | |||||
| … stopped | 31 | 42% | |||||
| visit | 73 | ||||||
| … v0 | 52 | 71% | |||||
| … v1 | 21 | 29% | |||||
| season | 73 | ||||||
| … spring | 14 | 19% | |||||
| … summer | 22 | 30% | |||||
| … autumn | 21 | 29% | |||||
| … winter | 16 | 22% | |||||
| breed_group | 73 | ||||||
| … ckcs | 7 | 10% | |||||
| … mix | 16 | 22% | |||||
| … other | 26 | 36% | |||||
| … pug | 7 | 10% | |||||
| … ret | 17 | 23% | |||||
| coat_colour | 73 | ||||||
| … dark | 30 | 41% | |||||
| … light | 28 | 38% | |||||
| … mix | 15 | 21% | |||||
| sex | 73 | ||||||
| … Female | 43 | 59% | |||||
| … Male | 30 | 41% | |||||
| age | 73 | 96 | 36 | 16 | 73 | 117 | 182 |
| comorbidity | 73 | ||||||
| … no | 15 | 21% | |||||
| … yes | 58 | 79% | |||||
| fat_percent | 55 | 40 | 7.8 | 18 | 37 | 45 | 61 |
| cortisol | 73 | 8.1 | 16 | 0.41 | 1.4 | 6.8 | 105 |
| lgCort | 73 | 1.2 | 1.2 | -0.88 | 0.34 | 1.9 | 4.7 |
| breed | 73 | ||||||
| … mix | 16 | 22% | |||||
| … ckcs | 7 | 10% | |||||
| … pug | 7 | 10% | |||||
| … ret | 17 | 23% | |||||
| … other | 26 | 36% |
par(mfrow = c(1,1))
vioplot(cortisol ~ season, col = "firebrick",
data = df)
par(mfrow = c(1,1))
vioplot(lgCort ~ season, col = "firebrick",
data = df)
stripchart(lgCort ~ season, vertical = TRUE, method = "jitter",
col = "steelblue3", data = df, pch = 20)
df$slgCort <- standardize(df$lgC)
summary(df$slgCort)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.7079 -0.6925 -0.2768 0.0000 0.6142 2.8713
hist(df$slgCort, breaks =20, col = "steelblue3", main = "Histogram of log hair cortisol", xlab = "Log hair cortisol (standardised)", xlim = c(-2, 3))
df2 <- na.omit(df)
model <- brm(slgCort ~ season + (1 | visit), family = skew_normal(), data = df)
default_prior(slgCort ~ season + (1 | visit),
family = skew_normal(),
data = df)
## prior class coef group resp dpar nlpar lb ub
## normal(0, 4) alpha
## (flat) b
## (flat) b seasonautumn
## (flat) b seasonsummer
## (flat) b seasonwinter
## student_t(3, -0.3, 2.5) Intercept
## student_t(3, 0, 2.5) sd 0
## student_t(3, 0, 2.5) sd visit 0
## student_t(3, 0, 2.5) sd Intercept visit 0
## student_t(3, 0, 2.5) sigma 0
## source
## default
## default
## (vectorized)
## (vectorized)
## (vectorized)
## default
## default
## (vectorized)
## (vectorized)
## default
Little evidence of effect of season on hair cortisol. In one study (Roth), hair cortisol in January was hoigher in Jauary compared with May and September. However, it was not clear how these sample points related to other times of year (e.g., summer monhths, ohter months in winter, spring and autumn), but subtle and not clear. Therefore, we elected to set a neutral regularising prior allowing the model to learn from the data. Might be safer just to use a regularising prior. However, could try an alternative with a slight winter effect
Roth LS, Faresjö Å, Theodorsson E, Jensen P. Hair cortisol varies with season and lifestyle and relates to human interactions in German shepherd dogs. Sci Rep. 2016 Jan 21;6:19631. doi: 10.1038/srep19631
# Set individual priors
prior_int <- set_prior("normal(0, 0.5)", class = "Intercept")
prior_sig <- set_prior("exponential(1)", class = "sigma")
prior_b <- set_prior("normal(0, 1)", class = "b")
prior_sd <- set_prior("normal(0, 1)", class = "sd")
prior_alpha <- set_prior("normal(4, 2)", class = "alpha")
# Combine priors into list
priors <- c(prior_int, prior_sig, prior_b, prior_sd, prior_alpha)
x <- seq(-3, 3, length.out = 100)
y <- dnorm(x, mean = 0, sd = 0.5)
plot(y ~ x, type = "l")
x <- seq(0, 3, length.out = 100)
y <- dexp(x, rate = 1)
plot(y ~ x, type = "l")
Increased adapt_delta >0.8 (0.9 here), as had divergent transitions
set.seed(666)
model <- brm(slgCort ~ season + (1 | visit),
family = skew_normal(),
prior = priors,
data = df,
control=list(adapt_delta=0.999, stepsize = 0.001, max_treedepth =15),
iter = 8000, warmup = 2000,
cores = 4,
save_pars = save_pars(all =TRUE),
sample_prior = TRUE)
## Compiling Stan program...
## Trying to compile a simple C file
## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## using C compiler: ‘Apple clang version 17.0.0 (clang-1700.0.13.5)’
## using SDK: ‘MacOSX15.5.sdk’
## clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/opt/R/arm64/include -fPIC -falign-functions=64 -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
## /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
## 679 | #include <cmath>
## | ^~~~~~~
## 1 error generated.
## make: *** [foo.o] Error 1
## Start sampling
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
## Found more than one class "stanfit" in cache; using the first, from namespace 'rethinking'
## Also defined by 'rstan'
summary(model)
## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: slgCort ~ season + (1 | visit)
## Data: df (Number of observations: 73)
## Draws: 4 chains, each with iter = 8000; warmup = 2000; thin = 1;
## total post-warmup draws = 24000
##
## Multilevel Hyperparameters:
## ~visit (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.36 0.36 0.01 1.35 1.00 7211 9113
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.08 0.31 -0.56 0.70 1.00 9968 11735
## seasonsummer -0.18 0.26 -0.67 0.33 1.00 12907 12966
## seasonautumn -0.32 0.27 -0.84 0.22 1.00 12768 13794
## seasonwinter 0.26 0.28 -0.29 0.82 1.00 12885 13103
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.99 0.09 0.83 1.19 1.00 15716 14164
## alpha 4.75 1.46 2.28 7.94 1.00 14979 14148
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
plot(model)
Looking for hairy caterpillars
mcmc_plot(model, type = 'rank_overlay')
Usually better than the compatability intervals given in the summary ### a. summer
draws <- as.matrix(model)
HPDI(draws[,2], 0.97) # 1st column is raws for age
## |0.97 0.97|
## -0.7345002 0.3749654
draws <- as.matrix(model)
HPDI(draws[,3], 0.97) # 1st column is raws for age
## |0.97 0.97|
## -0.8887980 0.2880951
draws <- as.matrix(model)
HPDI(draws[,4], 0.97) # 1st column is raws for age
## |0.97 0.97|
## -0.3419357 0.8846329
bayes_R2(model, probs = c(0.015, 0.5, 0.985)) # 0.015, 0.5, 0.985 are the quantiles
## Estimate Est.Error Q1.5 Q50 Q98.5
## R2 0.07947026 0.04182219 0.01072127 0.07424133 0.1849599
loo_R2(model, probs = c(0.015, 0.5, 0.985)) # 0.015, 0.5, 0.985 are the quantiles
## Estimate Est.Error Q1.5 Q50 Q98.5
## R2 -0.02536903 0.05524721 -0.1526872 -0.02368764 0.088321
checks whether actual data is similar to simulated data.
pp_check(model, ndraws = 100)
par(mfrow = c(1,1))
pp_check(model, type = "hist", ndraws = 11, binwidth = 0.25) # separate histograms of 11 MCMC draws vs actual data
pp_check(model, type = "error_hist", ndraws = 11) # separate histograms of errors for 11 draws
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
pp_check(model, type = "scatter_avg", ndraws = 100) # scatter plot
pp_check(model, type = "stat_2d") # scatterplot of joint posteriors
## Using all posterior draws for ppc type 'stat_2d' by default.
## Note: in most cases the default test statistic 'mean' is too weak to detect anything of interest.
# PPC functions for predictive checks based on (approximate) leave-one-out (LOO) cross-validation
pp_check(model, type = "loo_pit_overlay", ndraws = 1000)
## NOTE: The kernel density estimate assumes continuous observations and is not optimal for discrete observations.
pp_check(model, type = "error_scatter_avg")
## Using all posterior draws for ppc type 'error_scatter_avg' by default.
pairs(model)
loo_model <- loo(model, moment_match = TRUE)
loo_model
##
## Computed from 24000 by 73 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -100.7 6.1
## p_loo 5.3 1.1
## looic 201.4 12.1
## ------
## MCSE of elpd_loo is 0.0.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.5, 1.1]).
##
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.
First, check the sensitivity of the prior and likelihood to power-scaling. Posterior and posteriors resulting from power-scaling.
powerscale_sensitivity(model, variable = c("b_Intercept", "sigma", "b_seasonsummer", "b_seasonautumn", "b_seasonwinter"), facet_rows = "variable")
## Sensitivity based on cjs_dist
## Prior selection: all priors
## Likelihood selection: all data
##
## variable prior likelihood diagnosis
## b_Intercept 0.037 0.035 -
## sigma 0.035 0.146 -
## b_seasonsummer 0.009 0.091 -
## b_seasonautumn 0.020 0.091 -
## b_seasonwinter 0.011 0.075 -
powerscale_plot_dens(model, variable = c("b_Intercept", "sigma", "b_seasonsummer", "b_seasonautumn", "b_seasonwinter"), facet_rows = "variable")
powerscale_plot_ecdf(model, variable = c("b_Intercept", "sigma", "b_seasonsummer", "b_seasonautumn", "b_seasonwinter"), facet_rows = "variable")
powerscale_plot_quantities(model, vvariable = c("b_Intercept", "sigma", "b_seasonsummer", "b_seasonautumn", "b_seasonwinter"), facet_rows = "variable")
mean(model$data$slgCort)
## [1] -1.76419e-16
sd(model$data$slgCort)
## [1] 1
These values appear similar to what was set for the priors, so seems OK?
check_prior(model, effects = "all")
## Parameter Prior_Quality
## 1 b_Intercept informative
## 2 b_seasonsummer informative
## 3 b_seasonautumn informative
## 4 b_seasonwinter informative
## 5 sd_visit__Intercept informative
prior <- prior_draws(model)
prior %>% glimpse()
## Rows: 24,000
## Columns: 5
## $ Intercept <dbl> -0.16873777, -0.76254257, 0.72117808, -0.60843457, 0.3585218…
## $ b <dbl> 0.38628806, 2.23779242, 0.70207565, -0.70573365, 1.43807172,…
## $ sigma <dbl> 1.22757771, 0.11401542, 1.13981912, 1.96439820, 0.90385733, …
## $ alpha <dbl> 1.9628879, -0.2067883, 1.2664916, 5.0834548, 7.6534384, 4.95…
## $ sd_visit <dbl> 0.11822937, 0.59715140, 0.30821303, 0.15514865, 1.11922846, …
set.seed(5)
prior %>%
slice_sample(n = 50) %>%
rownames_to_column("draw") %>%
expand_grid(a = c(0, 1)) %>%
mutate(c = Intercept + b * a) %>%
ggplot(aes(x = a, y = c)) +
geom_line(aes(group = draw),
color = "firebrick", alpha = .4) +
geom_point(color = "firebrick", size = 2) +
labs(x = "Season",
y = "log(cort) (std)") +
coord_cartesian(ylim = c(-3, 3)) +
theme_bw() +
theme(panel.grid = element_blank())
Can simulate data just on the priors. Fit model but only consider prior when fitting model. If this looks reasonable, it helps to confirm that your priors were reasonable
set.seed(666)
model_priors_only <- brm(slgCort ~ season + (1 | visit),
family = skew_normal(),
prior = priors,
data = df,
sample_prior = "only")
## Compiling Stan program...
## Trying to compile a simple C file
## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## using C compiler: ‘Apple clang version 17.0.0 (clang-1700.0.13.5)’
## using SDK: ‘MacOSX15.5.sdk’
## clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/opt/R/arm64/include -fPIC -falign-functions=64 -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
## /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
## 679 | #include <cmath>
## | ^~~~~~~
## 1 error generated.
## make: *** [foo.o] Error 1
## Start sampling
##
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pp_check(model_priors_only, ndraws = 100)
as_draws_df(model) %>%
select(b_Intercept:sigma) %>%
cov() %>%
round(digits = 3)
## Warning: Dropping 'draws_df' class as required metadata was removed.
## b_Intercept b_seasonsummer b_seasonautumn b_seasonwinter
## b_Intercept 0.097 -0.041 -0.043 -0.043
## b_seasonsummer -0.041 0.065 0.039 0.039
## b_seasonautumn -0.043 0.039 0.073 0.040
## b_seasonwinter -0.043 0.039 0.040 0.078
## sd_visit__Intercept -0.004 0.002 0.003 0.005
## sigma 0.005 0.000 0.000 0.000
## sd_visit__Intercept sigma
## b_Intercept -0.004 0.005
## b_seasonsummer 0.002 0.000
## b_seasonautumn 0.003 0.000
## b_seasonwinter 0.005 0.000
## sd_visit__Intercept 0.129 0.001
## sigma 0.001 0.008
NB Uses posterior_predict
# use posterior predict to simulate predictions
ppd <- posterior_predict(model)
par(mfrow = c(2,2))
stripchart(slgCort ~ season, vertical = TRUE, method = "jitter",
col = "steelblue3", data = df, pch = 20, main = "Observed")
stripchart(ppd[sample(seq(1, dim(ppd)[1]), 1),] ~ season, vertical = TRUE, method = "jitter",
col = "firebrick3", data = df, pch = 20, main = "PPD")
stripchart(ppd[sample(seq(1, dim(ppd)[1]), 1),] ~ season, vertical = TRUE, method = "jitter",
col = "firebrick3", data = df, pch = 20, main = "PPD")
stripchart(ppd[sample(seq(1, dim(ppd)[1]), 1),] ~ season, vertical = TRUE, method = "jitter",
col = "firebrick3", data = df, pch = 20, main = "PPD")
plot(conditional_effects(model), ask = FALSE)
ce <- conditional_effects(model, effects = "season")
ce_df <- ce[[1]][c(1, 6:9)]
ggplot(ce_df, aes(x=season, y=estimate__, group=1)) +
geom_errorbar(width=.1, aes(ymin=lower__, ymax=upper__), colour=c("#F8766D", "#00BFC4","#7CAE00","#C77CFF"), linewidth = 1) +
geom_point(shape=21, size=6, fill=c("#F8766D", "#00BFC4","#7CAE00","#C77CFF")) +
theme_bw() +
labs(title = "Conditional effect of season on hair cortisol") +
labs(y = paste0("Log Hair Cortisol (standardised)")) +
labs(x = paste0("Season")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey25", size = 12),
axis.text.y = element_text(color = "grey50", size = 10))
mcmc_plot(model)
mcmc_plot(model,
variable = c("b_seasonsummer", "b_seasonautumn",
"b_seasonwinter", "prior_b"))
mcmc_plot(model,
variable = c("b_seasonsummer", "b_seasonautumn",
"b_seasonwinter", "prior_b"),
type = "areas") +
theme_classic() +
labs(title = "Prior vs posterior distribution for season effect") +
labs(y = "") +
labs(x = paste0("Possible parameter values")) +
scale_y_discrete(labels=c("prior_b" = "Prior", "b_seasonsummer" = "Summer posterior",
"b_seasonautumn" = "Autumn posterior", "b_seasonwinter" = "Winter posterior"),
limits = c("prior_b", "b_seasonsummer",
"b_seasonautumn", "b_seasonwinter")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey50", size = 12),
axis.text.y = element_text(color = "grey8",size = 12))
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
mcmc_plot(model,
variable = c(
"b_seasonsummer",
"b_seasonautumn",
"b_seasonwinter"))
posterior <- as.matrix(model)
mcmc_areas(posterior,
pars = c("b_Intercept",
"sigma",
"b_seasonsummer",
"b_seasonautumn",
"b_seasonwinter"),
# arbitrary threshold for shading probability mass
prob = 0.75)
posterior <- as.matrix(model)
mcmc_areas(posterior,
pars = c("b_seasonsummer",
"b_seasonautumn",
"b_seasonwinter"),
# arbitrary threshold for shading probability mass
prob = 0.97) +
theme_classic() +
labs(title = "Posterior distribution for season effect",
y = "Density distribution",
x = "Possible parameter values") +
scale_y_discrete(labels=c("b_seasonsummer" = "Summer",
"b_seasonautumn" = "Autumn", "b_seasonwinter" = "Winter")) +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey50", size = 12),
axis.text.y = element_text(color = "grey8",size = 12))
## Scale for y is already present.
## Adding another scale for y, which will replace the existing scale.
# Focus on describing posterior
hdi_range <- hdi(model, ci = c(0.65, 0.70, 0.80, 0.89, 0.95))
plot(hdi_range, show_intercept = T)
# Focus on describing posterior
hdi_range <- hdi(model, ci = c(0.65, 0.70, 0.80, 0.89, 0.95),
parameters = c("b_seasonsummer", "b_seasonautumn",
"b_seasonwinter"))
plot(hdi_range, show_intercept = T) +
labs(title = "Posterior distribution for season effect") +
labs(y = "Density distribution") +
labs(x = "Possible parameter values") +
theme(axis.title.y = element_text(size=12, face="bold"),
axis.title.x = element_text(size=12, face="bold"),
title = element_text(size=12, face="bold"),
plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(color = "grey50", size = 12),
axis.text.y = element_text(color = "grey8",size = 12))
draws <- as.matrix(model)
mean(draws[,2] >0)
## [1] 0.2339583
HPDI(draws[,2], prob=0.97)
## |0.97 0.97|
## -0.7345002 0.3749654
mean(draws[,2] >0)
## [1] 0.2339583
mean(draws[,2] <0)
## [1] 0.7660417
draws <- as.matrix(model)
mean(draws[,3] >0)
## [1] 0.117625
mean(draws[,3] <0)
## [1] 0.882375
HPDI(draws[,3], prob=0.97)
## |0.97 0.97|
## -0.8887980 0.2880951
draws <- as.matrix(model)
mean(draws[, 4] >0)
## [1] 0.8286667
mean(draws[,4] <0)
## [1] 0.1713333
HPDI(draws[, 4], prob=0.97)
## |0.97 0.97|
## -0.3419357 0.8846329
# create new dataframe which contains results of the first dog
new_data <- rbind(df[1,], df[1,], df[1,], df[1,])
# Now change one category to be different
new_data$season <- c("autumn", "winter", "spring", "summer")
# Visualise df to make sure it has worked
new_data
## number group visit season breed_group coat_colour sex age comorbidity
## 1 c1 stopped v0 autumn ret dark Male 43 yes
## 2 c1 stopped v0 winter ret dark Male 43 yes
## 3 c1 stopped v0 spring ret dark Male 43 yes
## 4 c1 stopped v0 summer ret dark Male 43 yes
## fat_percent cortisol lgCort breed slgCort
## 1 52.21393 4.92422 1.594166 ret 0.3415375
## 2 52.21393 4.92422 1.594166 ret 0.3415375
## 3 52.21393 4.92422 1.594166 ret 0.3415375
## 4 52.21393 4.92422 1.594166 ret 0.3415375
# Now get mean predictions from the draws of the model
pred_means <- posterior_predict(model, newdata = new_data)
# Compare difference in means for each season versus Autumn
differenceWinter <- pred_means[,1] - pred_means[,2]
par(mfrow = c(2,2))
# Examine mean of difference
mean(differenceWinter)
## [1] -0.5704704
# View histogram of this
hist(differenceWinter)
# Create HPDI
HPDI(differenceWinter, 0.97)
## |0.97 0.97|
## -3.769518 2.672875
# Compare difference in means for each season versus Autumn
differenceSpring <- pred_means[,1] - pred_means[,2]
par(mfrow = c(2,2))
# Examine mean of difference
mean(differenceSpring)
## [1] -0.5704704
# View histogram of this
hist(differenceSpring)
# Create HPDI
HPDI(differenceSpring, 0.97)
## |0.97 0.97|
## -3.769518 2.672875
# Compare difference in means for each season versus Autumn
differenceSummer <- pred_means[,1] - pred_means[,2]
par(mfrow = c(2,2))
# Examine mean of difference
mean(differenceSummer)
## [1] -0.5704704
# View histogram of this
hist(differenceSummer)
# Create HPDI
HPDI(differenceSummer, 0.97)
## |0.97 0.97|
## -3.769518 2.672875
# create new dataframe which contains results of all dogs
new_data1 <- df
# Now change one category to be different
new_data1$season <- c("spring")
# create new dataframe which contains result sof all dogs
new_data2 <- df
# Now change one category to be different
new_data1$season <- c("summer")
# Now get predictions from the draws of the models
pred_nd1 <- posterior_predict(model, newdata = new_data1)
pred_nd2 <- posterior_predict(model, newdata = new_data2)
pred_diff <- pred_nd1 - pred_nd2
pred_diff <- data.frame(pred_diff)
# Create mean of differences for each column (dog) of the dataframe
pred_diff_summer <- apply(pred_diff, 2, mean)
# View histogram of mean differences
hist(pred_diff_summer)
# Examine mean of difference
mean(pred_diff_summer)
## [1] -0.09230316
# View histogram of this
HPDI(pred_diff_summer, 0.97)
## |0.97 0.97|
## -0.4605680 0.1528126
# create new dataframe which contains results of all dogs
new_data1 <- df
# Now change one category to be different
new_data1$season <- c("spring")
# create new dataframe which contains result sof all dogs
new_data2 <- df
# Now change one category to be different
new_data1$season <- c("autumn")
# Now get predictions from the draws of the models
pred_nd1 <- posterior_predict(model, newdata = new_data1)
pred_nd2 <- posterior_predict(model, newdata = new_data2)
pred_diff <- pred_nd1 - pred_nd2
pred_diff <- data.frame(pred_diff)
# Create mean of differences for each column (dog) of the dataframe
pred_diff_autumn <- apply(pred_diff, 2, mean)
# View histogram of mean differences
hist(pred_diff_autumn)
# Examine mean of difference
mean(pred_diff_autumn)
## [1] -0.2325993
# View histogram of this
HPDI(pred_diff_autumn, 0.97)
## |0.97 0.97|
## -0.59590142 0.01702301
# create new dataframe which contains results of all dogs
new_data1 <- df
# Now change one category to be different
new_data1$season <- c("spring")
# create new dataframe which contains result sof all dogs
new_data2 <- df
# Now change one category to be different
new_data1$season <- c("winter")
# Now get predictions from the draws of the models
pred_nd1 <- posterior_predict(model, newdata = new_data1)
pred_nd2 <- posterior_predict(model, newdata = new_data2)
pred_diff <- pred_nd1 - pred_nd2
pred_diff <- data.frame(pred_diff)
# Create mean of differences for each column (dog) of the dataframe
pred_diff_winter <- apply(pred_diff, 2, mean)
# View histogram of mean differences
hist(pred_diff_winter)
# Examine mean of difference
mean(pred_diff_winter)
## [1] 0.3527753
# View histogram of this
HPDI(pred_diff_winter, 0.97)
## |0.97 0.97|
## -0.0113434 0.6059657
pred_slgCort <- posterior_epred(model)
av_pred_slgCort <- colMeans(pred_slgCort)
plot(av_pred_slgCort ~ df$slgCort)
# Set individual priors
prior_int <- set_prior("normal(0, 0.5)", class = "Intercept")
prior_b <- set_prior("normal(0, 1)", class = "b")
prior_sd <- set_prior("normal(0, 1)", class = "sd")
prior_alpha <- set_prior("normal(4, 2)", class = "alpha")
# Combine priors into list
priors2 <- c(prior_int, prior_b, prior_sd, prior_alpha)
Increased adapt_delta >0.8 (0.9 here), as had divergent transitions
set.seed(666)
model2 <- brm(bf(slgCort ~ season + (1 | visit),
sigma ~ season),
family = skew_normal(),
prior = priors2,
data = df,
control=list(adapt_delta=0.99),
save_pars = save_pars(all =TRUE),
sample_prior = TRUE)
## Compiling Stan program...
## Trying to compile a simple C file
## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## using C compiler: ‘Apple clang version 17.0.0 (clang-1700.0.13.5)’
## using SDK: ‘MacOSX15.5.sdk’
## clang -arch arm64 -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DUSE_STANC3 -DSTRICT_R_HEADERS -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION -D_HAS_AUTO_PTR_ETC=0 -include '/Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/opt/R/arm64/include -fPIC -falign-functions=64 -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp:22:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/Core:19:
## /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:679:10: fatal error: 'cmath' file not found
## 679 | #include <cmath>
## | ^~~~~~~
## 1 error generated.
## make: *** [foo.o] Error 1
## Start sampling
##
## SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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summary(model2)
## Family: skew_normal
## Links: mu = identity; sigma = log; alpha = identity
## Formula: slgCort ~ season + (1 | visit)
## sigma ~ season
## Data: df (Number of observations: 73)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~visit (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.37 0.37 0.01 1.37 1.00 1583 2075
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.12 0.33 -0.52 0.78 1.00 1734 2294
## sigma_Intercept 0.03 0.20 -0.32 0.43 1.00 1893 2392
## seasonsummer -0.28 0.31 -0.91 0.30 1.00 1842 2061
## seasonautumn -0.23 0.35 -0.92 0.45 1.00 1927 2312
## seasonwinter 0.22 0.33 -0.45 0.85 1.00 2094 2467
## sigma_seasonsummer -0.14 0.26 -0.64 0.36 1.00 1848 2397
## sigma_seasonautumn 0.10 0.26 -0.41 0.59 1.00 1899 2355
## sigma_seasonwinter -0.06 0.28 -0.61 0.46 1.00 2022 2576
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## alpha 4.84 1.43 2.29 7.88 1.00 3386 2887
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
loo_model2 <- loo(model2, moment_match = TRUE)
loo_model2
##
## Computed from 4000 by 73 log-likelihood matrix.
##
## Estimate SE
## elpd_loo -102.9 6.1
## p_loo 7.6 1.3
## looic 205.9 12.1
## ------
## MCSE of elpd_loo is 0.1.
## MCSE and ESS estimates assume MCMC draws (r_eff in [0.4, 1.2]).
##
## All Pareto k estimates are good (k < 0.7).
## See help('pareto-k-diagnostic') for details.
model <- add_criterion(model, "loo")
model2 <- add_criterion(model2, "loo")
## Warning: Found 1 observations with a pareto_k > 0.7 in model 'model2'. We
## recommend to set 'moment_match = TRUE' in order to perform moment matching for
## problematic observations.
loo_compare(model, model2)
## elpd_diff se_diff
## model 0.0 0.0
## model2 -2.3 1.0